WILMINGTON, Del. — President Barack Obama on Saturday eulogized Beau Biden, the former Delaware attorney general and oldest son of Vice President Joe Biden, as a one-of-a-kind politician and man, connected to but even better than his father, who the teary president called “my brother.”

“A man is original when he speaks the truth that has always been known to all good men,” Obama said at the funeral, quoting the Irish poet Patrick Kavanagh.

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“Beau Biden was an original,” Obama said. “He was a good man. A man of character. A man who loved deeply and was loved in return.”

He spoke of Biden’s service in the military, his work as attorney general but most of all his place as a devoted member of a family that Obama acknowledged had once again met “faceless, seemingly random cruelty.”

The Biden family arrived to St. Anthony of Padua church here in the morning by foot, huddled together as if in a giant embrace, the vice president leading them, holding his daughter-in-law’s hand with his right hand while she held his grandson Hunter’s hand on her other side. The vice president held the hand of his granddaughter Natalie with his left hand, with Dr. Jill Biden holding her other hand.

Just before the door to the hearse opened, the vice president briefly looked to the sky. As they saw the flag-covered coffin, he bowed his head, kissed his daughter-in-law on hers, and then reached around to gently rub his grandson’s. Biden’s own son Hunter, standing right behind them, reached forward and wrapped his arm around his nephew.

As the casket was lifted out and began its path to the church, the vice president briefly put the palm of his hand over his heart.

After the casket entered, the family waited for it to make its way through the church. They shifted positions, and the vice president kissed Natalie and placed her hand in her mother’s. He took one step back and took his own wife’s hand. As they waited, he leaned forward and kissed his grandson’s head again.

The first chords of “Bring Him Home,” from “Les Miserables” began to play, and the vice president crossed himself as he prepared to enter.

Beau Biden died last Saturday of brain cancer. His funeral comes after a week of mourning, with the vice president and his family staying for hours at a service Thursday in Dover, where his son lay in honor, with the family then spending 10 hours at the church here Friday, receiving fellow mourners until 11 P.M. Some waited in line six hours to see them.

Saturday morning, politicians from across the generations gathered at the church, including the first family, most of the Obama Cabinet, former President Bill Clinton and Secretary of State Hillary Clinton, current and former members of Congress, and a crowd of 1,000 friends, family, and current and former White House and Biden staff. A crowd of Delawareans gathered outside, some sharing memories as the service began inside — waiting for the full service, even though they could not hear or see any of it, aside from the livestream that some played on their cellphones.

Some arrived by Amtrak, appropriately enough, taking the same ride from Washington, D.C. to Wilmington that Biden used to take every night as a young senator to spend as much times as possible with his sons.

Obama’s voice broke as he spoke of his love for Beau and Joe Biden and the whole Biden family, of which he said he and his the first lady had come to consider themselves honorary members.

“We’re always here for you, we always will be. My word as a Biden,” Obama said.

After he finished, Obama walked to hug the vice president, holding him in an embrace and whispering a few words. Obama kissed him on the cheek, and then hugged Beau Biden’s wife, Hallie.

“Beau Biden’s character was genuine. He had a natural charisma that few people possess. People willing wanted to follow him, trusted his judgment and believed in him,” said Gen. Ray Odierno, recalling Biden’s service in the National Guard, and saying he had expected Biden to one day be president and was thrilled at the prospect. “Beau possessed the traits I have witnessed only in the greatest leaders.”

Odierno presented Biden posthumously with the Legion of Merit at the service.

“Although Beau’s life was much too short, his legacy will live on in the thousands he touched, the thousands he influenced and the many he loved,” Odierno said.

The vice president’s other children, Hunter and Ashley, eulogized their brother.

“We will all always be one family because we always have been one family,” Hunter Biden said, speaking to his brother’s children.

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He spoke of his first memory, at three years old, his brother — then just four years old himself — holding his hand in the hospital room where they were recovering from the car crash that killed his mother and sister. Beau Biden was staring into his eyes, saying “I love you, I love you, I love you,” over and over again.

“And in the 42 years since, he never stopped holding my hand, he never stopped telling me just how much he loves me. But mine wasn’t the only hand Beau held. Beau’s was the hand everyone reached for in their time of need,” Hunter Biden said.

Last week, Hunter Biden said, the whole Biden family surrounded Beau as he died, holding onto him, telling him they loved him.

“The reaction has been universal,” said Rev. Leo O’Donovan, the president emeritus of Georgetown University, who is the celebrant of the Catholic funeral. “Whether you were a friend of Beau Biden’s or only knew him from the press. How sad. How very, very sad.”

What set Beau Biden apart, Obama said, was that he wasn’t defined by the tragedies he’d survived in his life and he didn’t rely on his family name.

“He even looked and sounded like Joe, though I think Joe would be the first to acknowledge that Beau was an upgrade: Joe 2.0,” Obama said. “He did in 46 years what most of us couldn’t do in a lifetime. He left nothing in the tank.”

Obama said that is what people should take forward from the life they remembered Saturday.

“It is our obligation — and our obligation to Beau,” Obama said, “not to think about what was and what might have been, but instead think about what is because of him.”